We use techniques usually associated with data inversion to analyse a Fredholm integral equation of the first kind for the forward modelling of acoustic scattering by a 2-D body with Dirichlet boundary conditions. The `data' are the incident field values on the body, the unknown `model' is the derivative of the total field on the surface, and there is a a singular Hankel function kernel. We compute the inner product matrix elements and invert to get the surface field derivative, which matches the classical solution for the simple case of the circular cylinder. Grid resolution and node placement requirements are investigated via standard inverse theory approaches, including: